Highest Common Factor of 218, 8673 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 218, 8673 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 218, 8673 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 218, 8673 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 218, 8673 is 1.
HCF(218, 8673) = 1
HCF of 218, 8673 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 218, 8673 is 1.
Highest Common Factor of 218,8673 is 1
Step 1: Since 8673 > 218, we apply the division lemma to 8673 and 218, to get
8673 = 218 x 39 + 171
Step 2: Since the reminder 218 ≠ 0, we apply division lemma to 171 and 218, to get
218 = 171 x 1 + 47
Step 3: We consider the new divisor 171 and the new remainder 47, and apply the division lemma to get
171 = 47 x 3 + 30
We consider the new divisor 47 and the new remainder 30,and apply the division lemma to get
47 = 30 x 1 + 17
We consider the new divisor 30 and the new remainder 17,and apply the division lemma to get
30 = 17 x 1 + 13
We consider the new divisor 17 and the new remainder 13,and apply the division lemma to get
17 = 13 x 1 + 4
We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get
13 = 4 x 3 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 218 and 8673 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(17,13) = HCF(30,17) = HCF(47,30) = HCF(171,47) = HCF(218,171) = HCF(8673,218) .
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Frequently Asked Questions on HCF of 218, 8673 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 218, 8673?
Answer: HCF of 218, 8673 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 218, 8673 using Euclid's Algorithm?
Answer: For arbitrary numbers 218, 8673 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.